A junior government minister says it's 'scandalous' that people have jumped the vaccine queue.
The HSE has acknowledged there have been cases of people skipping the queue.
CEO Paul Reid said such cases have been exceptions, but the public anger over them is 'understandable'.
It comes in the wake of the controversy last week over 20 private school teachers being given leftover vaccines by the Beacon Hospital.
Separately, The Irish Daily Mail reported this week that the HSE's online vaccine booking system for frontline staff had been 'abused' by some non-healthcare workers to skip the queue.
On The Pat Kenny Show, Patrick O'Donovan - Minister of State with responsibility for the OPW - says it's hard to defend situations where people don't wait their turn.
He said: “I think it’s scandalous that there has been queue jumping, and that we’ve seen the situation we have seen.
“I’ve had people onto my office on the frontline who feel hard done by… I’ve had family carers who are locked into their houses for the last 13 months, and who can’t get out and feel really aggrieved… my heart breaks for them."
Green Party Senator Pippa Hackett, meanwhile, said it's clear the system hasn't worked properly to prevent cases of people cheating the system.
She said that should change following the major overhaul of the vaccine rollout, which will see the priority list switch to an age-based system once vulnerable groups are vaccinated.
Senator Hackett said she understands why teacher and garda unions feel aggrieved that their members now won't be prioritised.
However, she observed: "Do I believe that a 30-year-old garda or teacher [wouldn't] stand in front of their 60-year-old parent for a vaccine? I don't.
"The HSE has indicated it will be more straightforward to do it this way, and we won't have people jumping the queue in the way we have seen up until now."